Webcasts for Educators
Student Achievement Division
Viewer’s Guide
Teaching Mathematics
Through a Social Justice Lens
Multi-media resource for professional learning
On this DVD you will find a Print and Video Resources folder which
contains WMV files for PowerPoint presentations, this Viewer’s Guide (PDF)
and the LNS monographs Integrated Learning in the Classroom and
Integrated Curriculum.
To order:
Webcasts for Educators – Teaching Mathematics Through a Social
Justice Lens
Contact ServiceOntario
416-326-5300 or 1-800-668-9938
http://www.publications.serviceontario.ca/ecom
The webcast segments and related resources are also accessible online at
www.curriculum.org/secretariat/justice
This resource may be copied for not-for-profit educational purposes.
Funded by the Student Achievement Division, Ontario Ministry
of Education.
Table of Contents
Overview........................................................................................ 3
From Viewing to Action .................................................................... 4
VIDEO SEGMENTS
What is social justice math?............................................................. 4
Building a Collaborative Culture of Learning........................................ 5
Job-Embedded Professional Learning.............................................. 5
• Setting the Context.................................................................... 5
• Doing the Math........................................................................... 6
• Gallery Walk............................................................................... 7
• Being in the Learner’s Role........................................................ 8
• Consolidation............................................................................. 9
• Teacher Reflections.................................................................... 9
Professional Learning Session Debrief............................................. 10
• Shared Leadership..................................................................... 10
• Collaborative Inquiry................................................................. 10
• Building a Culture of Learning................................................... 10
Social Justice Math Lesson............................................................... 11
• Activating Prior Knowledge............................................................. 11
• Solving the Lesson Problem............................................................ 11
• Accountable Talk............................................................................. 12
• Analysis of Student Work................................................................ 12
• Consolidation.................................................................................. 13
Insights into Intense Learning........................................................... 14
• Student Reflections......................................................................... 14
• Teacher Reflections......................................................................... 14
Resources and Related Reading........................................................ 14
Technical Instructions ..................................................................... 15
• How to Access the Print and Video Resources................................ 15
• How to Save the Video Files to Your Computer.............................. 16
• How to Insert Video Clips (WMV files) into
a PowerPoint Presentation.............................................................. 17
“
…teachers need to spend more time and energy understanding learning through
the eyes of students.
”
Hattie, 2009
Overview
This resource shares one school’s approach to improving student learning in
mathematics – an approach called “social justice math” which involves
working with real numbers to solve real problems. The video follows both the
job-embedded professional learning at the school as well as an actual classroom
lesson. Enthusiasm, in-depth dialogue and commitment to learning are evident
during these sessions, as students and teachers take on the role of co-learners.
During the professional learning session, teachers take on the role of students
as they “learn the math by doing the math.” They participate in a three-part
math lesson about an autism fundraiser and gain insight into the impact of their
pedagogy on student learning. The principal and staff create a culture that is
open to learning, invites risk taking and celebrates the collaborative building of
new knowledge.
The teachers’ learning is then applied in the classroom in a three-part lesson in
mathematics. Students investigate fair trade, child labour and their own role as
consumers and responsible citizens. Student inquiry integrates the arts,
language, social studies and mathematics. They study in various groupings,
learning how to work and communicate as part of a team. What they learn
changes the way they think and the way they behave.
Throughout this resource, you will hear the classroom teacher, principal and
students speak of the power of teaching and learning mathematics through a
social justice lens. The principal speaks of empowering teachers, the teachers
speak of empowering students and the students speak of their own sense of
empowerment. Students begin to understand that they can each make a
difference and want to spread that sense of power to their family and
community.
“
When schools teach for wisdom, they teach students that it is important not just
what you know, but how you use what you know – whether you use it for good or bad
ends … Students learn to think wisely and understand things from diverse points
of view.
”
Sternberg, 2003, pp. 7–8
3
From Viewing to Action
As you watch the professional learning session, what evidence do you see of a
collaborative learning culture? How might your observations impact your
practice? You may wish to record your thinking and the connections you are
making to your own practice using the organizer depicted below.
Organizer #1 — Collaborative Learning Culture
Elements of a
Collaborative
Learning Culture
Evidence
Teams are continually
learning how to learn together.
Administrators along
with teachers are
learners – questioning,
investigating, reflecting
and seeking solutions.
What actions will you take to
support staff in becoming a
community focused on
continuous inquiry and
improvement?
Teams have a core of
shared beliefs and values.
*NOTE: Organizer #1 is available in Word and in PDF in the Print Resources folder on the DVD.
VIDEO Segments
What is social justice math?
(8:47)
Grade 5 teacher Alicia Gunn speaks about the power of teaching mathematics
through a social justice lens. She describes her integrated approach to engaging
children with real numbers and authentic scenarios that present problems
relevant to their lives.
4
•
•
•
•
•
Comment on the views presented by this teacher.
What do you see as the benefits of this approach to teaching mathematics?
What do you see as potential challenges?
How might you address these challenges?
How might you support students in learning how to negotiate personal
meaning between existing ideas and new ideas?
Building a Collaborative Culture
of Learning
Job-Embedded Professional Learning
Setting the Context
(2:26)
The principal and teacher set the context for this professional learning
session. The principal briefly welcomes the staff and the teacher highlights the
importance of social justice mathematics.
• Comment on the impact this introduction plays in this professional learning
session.
“
These (authentic) tasks, when strategically coordinated, present opportunities for
students to: discover new ideas; develop thinking skills; synthesize understanding;
transfer knowledge and skills from one subject to another; and demonstrate what they
know and think about their world and themselves as learners.
”
Capacity Building Series — Integrated Learning in the Classroom
• Discuss the above quote in light of the approach this teacher has taken.
• What role do curriculum expectations and the big ideas in mathematics play in
problem selection/design?
5
Doing the Math
(4:29)
Please take a moment to solve the following problem in a variety of ways.
The Race for Autism Problem:
The Race for Autism event is in San Diego. Your job is to design the 60 km race course.
Here is a list of what we will need on the course. Label each clearly:
•
•
•
•
•
•
•
•
a start line
a hotel halfway through the course
rest stations at every eighth of the course
food stations at every fourth of the course
water stations at every tenth of the course
media stations at every fifth of the course
kilometre markers placed along the way to indicate distance covered and
distance remaining
a finish line
• How does solving the problem help to unpack and contribute to the
development of your own understanding of the mathematics found in
the problem?
Teachers work with their math partners to “do the math.” During this
experience they take on the role of students as well as teachers solving the
lesson problem. Math partners continue to look through the teacher’s and the
students’ lens, relating their new insights to their pedagogy and to what they
know about how students learn mathematics.
• Using the following organizer, think about the conditions that support this
intense “learning the math by doing the math.”
6
Organizer #2 — Conditions That Support “Learning the Math by Doing the Math”
principal
support
risk-free
environment
Learning the math by
doing the math
*NOTE: Organizer #2 is available in Word and in PDF in the Print Resources folder on the DVD.
Gallery Walk
(2:33)
There are several approaches to gallery walk. This form is called a “stay and
stray” strategy. One person on the team stays with the work to explain to their
peers while the others circulate.
During a gallery walk, math partners examine the work of their peers,
considering strategies that are similar to or different from what they used to
solve the problem. During the gallery walk, participants are able to take ideas
they value and use them to refine or extend their own thinking. Experiencing
and debriefing the gallery walk provides teachers with insights as to the impact
of this strategy on student learning.
7
Organizer #3 — Gallery Walk
Aspects of the Gallery Walk Experience
Habit of Mind
•
•
•
•
•
•
open-mindedness
considering ideas of others
sharing ideas
altering one’s own thinking
reconsidering one’s thinking
building on the ideas of others
clearly communicating ideas in
written and oral form
•
•
•
*NOTE: Organizer #3 is available in Word and in PDF in the Print Resources folder on the DVD.
•
•
•
What norms would you establish in order to set your students or staff up for a
successful gallery walk?
Comment on how the gallery walk experience supports the development of the
habits of mind necessary for success in the real world.
What opportunities for assessment does a gallery walk offer teachers as they
observe their students?
Being in the Learner’s Role
(2:30)
As teachers collaborate to solve the lesson problem, they engage in accountable
talk to clarify their own thinking. Being in the learner’s role informs the teachers
as to the learning challenges some students might experience. Reflecting on the
problem and hearing various ways of solving the problem helps teachers unpack
their mathematical understandings and the mathematics involved in the problem.
These new insights help teachers improve their classroom practice.
“
The biggest effects on student learning occur when teachers become learners of
their own teaching and when students become their own teachers.
”
Hattie, 2009
8
•
•
•
As you view this video, record what you notice about the existing culture that
permits authentic job-embedded learning.
What actions would you take as a facilitator to help teachers articulate their own
learning, so that they continue to become consciously skilled?
What steps might you take to involve staff in collaborative, inquiry-based
professional learning?
Consolidation
(4:06)
During the consolidation phase of the lesson, facilitators select key mathematical
learning that they noticed in the teachers’ work. Math partners share with the
group their thinking with reference to their written work. During the sharing, the
facilitators ask probing questions to deepen the thinking of the presenters and the
class. They highlight and summarize the key points.
•
•
•
How might doing the math and predicting student responses support teachers in
remaining flexible during the consolidation phase of the lesson?
How might the teacher determine whether his/her teaching has been successful?
How might the teacher help students to determine their own success?
Teacher Reflections
(5:42)
Math partners talk about how it feels to be a doer of math. They reflect on how
doing the math helps them to be more empathetic to their students.
•
•
•
•
How do these teachers feel about being doers of math?
How might the experience of doing the math help you give your students a voice
in the mathematics classroom?
As you watched this segment, what resonated with you?
What actions might you take as a result of this viewing experience?
“
What makes strategies successful … teachers talking with other teachers about
teaching and planning, deliberate attention to learning intentions and success criteria
and … feedback information as to the success of their teaching on their students.
”
Hattie, 2009
9
Professional Learning Session Debrief
This collaborative learning session was focused on a problem of practice
identified by the staff. Participants included the administrators, teachers,
support staff and also external staff. After the session, participants met to reflect
on the culture of their school, their own learning and possible next steps.
Shared Leadership
(2:48)
•
•
What conditions do you think need to be in place in order for a shared leadership
approach to be successful?
What key messages might you share with your staff that would promote shared
leadership?
Collaborative Inquiry
(2:06)
• What do you see as the benefits of teachers assuming an inquiry stance as part of
their daily practice?
Building a Culture of Learning
(2:31)
• How might you continue to build partnerships for learning within and beyond
your school environment?
10
Social Justice Math Lesson
Activating Prior Knowledge
(12:41)
The teacher sets the context for the lesson problem by activating prior
knowledge about child labour and the cost of goods, minimum wage and fair
working conditions. The problem becomes relevant to students when talk
centres on the origin of the shoes they are wearing and the impact of their
decisions as consumers. Students are actively involved in examining their shoes,
noting information on a world map and then analyzing their data.
•
•
•
Comment on how this task addresses diverse learning styles.
How might you broaden the scope of this inquiry at this stage of the learning?
As you explore the social justice issue at hand, how might you dialogue with
students in a way that avoids framing people as “the other”? How might you
make students aware of the danger of this tendency so that they can
self-regulate?
Solving the Lesson Problem
(6:08)
Students work with their math partners to collaboratively solve the lesson
problem. They respectfully listen to each other and record their thinking in
order to share with their peers during their accountable sharing time. Students
practise their math communication skills as they express their ideas orally and
in written form. They check their work and try to discover the most efficient
way to solve the problem. The teacher circulates and collects data to assist in
determining next steps. She asks probing questions to stretch student thinking.
•
•
•
•
How might you help students develop their questioning skills to reflect a critical
stance?
Talk and interaction are essential for learning to take place. How might you
ensure that the talk is on-task and the math partner interaction is pushing
everyone’s learning forward?
Comment on how you might help students become more aware of the relevance
of their learning.
Identify and discuss the dynamics that exist between the mathematics content
and the social justice context.
11
Accountable Talk
(4:39)
During this sharing time, students clarify their thinking and consider multiple
ways of solving the lesson problem. One member of the math team stays with
the work to offer explanations and receive feedback. All other math partners
circulate to examine the math work of their peers. During this walk-about,
students ask questions, make recommendations or gather ideas to improve
their own work. The teacher walks around, listening in on the conversation
and occasionally joining in to ask a probing question for clarification or to
push student thinking forward. During this observation, the teacher gathers
information on which students need extra support or greater challenge.
The teacher determines which students will share their work during the
consolidation part of the lesson. At the end of the sharing time, partners
return to their own work, discuss their findings with their partner and make
adjustments based on peer feedback and their walk-about observations. They
prepare to share their work with the class.
•
•
•
What lifelong habits of mind do you think this strategy helps students develop?
How would you ensure that each student has a voice in this phase of the
learning?
How might you help students assess when ideas have substance and relevance
and when they do not?
“
It is through interactions with other students as well as with the teacher, and with
the opportunity to articulate their own thoughts, that students are able to construct
new
mathematical knowledge.
Small, 2009
”
Analysis of Student Work
(11:11)
The teachers analyse student work to determine the degree of mathematical
understanding reflected in the samples. The teachers select which work will be
shared and in which sequence – during the whole-group, highlight or summary
part of the lesson. This analysis also provides the teacher with valuable insight
into the learning needs of her students.
12
•
•
•
Discuss the role of mathematical big ideas and curriculum expectations in
supporting teacher analysis of students’ work in mathematics.
What advice might you give to someone just beginning to analyse student
work?
What questions might you ask of the work, of the student, of yourself as you
analyse student work to determine next steps?
Consolidation
(9:39)
Students come together as a whole class to discuss their new learning. They talk
about what they think is fair for workers to earn in order to meet their basic
needs. The teacher then invites several math partners to share their work.
“
Students’ actual opportunities to learn depend not only on the type of mathematical
tasks that teachers pose but also on the kinds of classroom discourse that takes place
during problem solving, both between the teacher and students and among students.
Discourse refers to the ways of representing, thinking, talking, and agreeing and
disagreeing that teachers and students use to engage in instructional tasks.
Students develop, represent, and justify their mathematical and strategic thinking,
deepening their conceptual understanding as they do so. In support of these learning
processes, the role of the teacher becomes one of a ‘mathematical mediator’ who
supports, probes, and negotiates valid mathematical thinking. Through questioning,
the teacher aims to illuminate and clarify student thinking, and helps students identify
any errors in reasoning while making sense of alternate strategies. •
•
•
”
National Council of Teachers of Mathematics, 2010
Comment on the consolidation phase of the lesson in light of the above quote.
What actions would you take to ensure that students at varying stages of
understanding all benefit from the consolidation phase of the lesson?
From the social justice aspect of the learning, how might you help students
recognize and take action against existing bias and stereotypes in our everyday
language and thinking?
13
Insights into Intense Learning
Student Reflections
(3:29)
Students discuss the ideas about learning mathematics through a social justice lens.
They feel empowered that they as individuals can make a difference.
Having confidence and feeling empowered are states of mind that need to be balanced
with a common-sense understanding of what is age-appropriate and possible.
•
•
What have you done or might you do to ensure that your students’ learning is
action-oriented with safe and attainable goals?
How might you further support these students in developing the skills with
which to communicate their ideas clearly and effectively?
Teacher Reflections
(8:19)
Alicia Gunn speaks about the power of teaching mathematics through a social
justice lens.
• Which ideas from her reflections resonate with you in light of your own practice?
• What questions do you have that you would like to investigate further?
Resources and Related Reading
Hattie, J. (2009). Visible learning. London: Routledge.
Literacy and Numeracy Secretariat. (2010). Capacity Building Series No. 14
– Integrated learning in the classroom.
Sternberg, R. (2003). What is an expert “student”? Educational Researcher, 32(8).
National Council of Teachers of Mathematics (NCTM). (2010). Why is teaching with
problem solving important to student learning? Reston, VA.
Small, M. (2009). Making math meaningful to Canadian students, K–8. Toronto:
Nelson Education.
14
Technical Instructions
How to Access the Print and Video Resources
To access the Print and Video Resources folder in Windows, insert the DVD
into the DVD drive of your computer and:
1. Click on the Start menu.
2. Select My Computer.
3. Right-click the mouse on the DVD icon titled
SOCIAL_JUSTICE_MATH_DVD to open a drop-down options list.
4. From the drop-down list, select and click on the Open option.
5. Double-click on the folder titled Print and Video Resources to access the
files. Ignore the folders titled Audio_TS and Video_TS.
6. Select the resources you wish to use directly from this folder,
OR Copy onto the Desktop and open files from the Desktop.
Alternatively, when the DVD is inserted and the options box opens:
1. Select the option Open Folder to View Files.
2. Click on the Print and Video Resources folder.
3. Select the files you wish to use directly from this folder, OR
Copy the files onto the Desktop and open them from the Desktop.
To access the Print and Video Resources folder in Mac OS X, insert the DVD
into the DVD drive of your computer and:
1. Exit from the DVD player (which typically opens automatically when a DVD
is inserted in the drive).
2. Double-click on the DVD icon titled SOCIAL_JUSTICE_MATH_DVD 3. Select the files you wish to use directly from this folder, OR
4. Copy the files onto the Desktop and open them from the Desktop.
15
How to Save the Video Files to Your Computer
The video files can all be copied and saved to your computer using either of
the following methods for copying and pasting files.
Method 1
1. Right-click on the file and choose the Copy option.
2. R
ight-click within any computer folder into which you would like to save
the file, and choose the Paste option.
Method 2
1. L
eft-click the mouse on the file you want to save, so that the file is
highlighted.
2. S
imultaneously press the Ctrl and C keys (or, for Macintosh users, the
Command and C keys) to copy the file.
3. L
eft-click within any computer folder in which you would like to save the
file, and simultaneously press the Ctrl and V keys (or, for Macintosh users,
the Command and V keys) to paste the file there.
For Macintosh users, the Command key is the one with the following
symbol:
NOTE: If you want to insert video files into a PowerPoint presentation, you must
save these video files in the same folder that contains your PowerPoint file. If
you save a PowerPoint presentation to another location (e.g., a memory stick,
CD-ROM, etc.), you must also save the video files in the same location in order
for the video to play. So, if you transfer the presentation to another computer,
you must also transfer the video files with it, or else the video will not link to the
PowerPoint presentation.
16
How to Insert Video Clips (WMV files) into a PowerPoint Presentation
On this DVD, you will find WMV versions of all segments of the webcast. To
insert a clip into a PowerPoint presentation, follow the directions below:
1. Open your PowerPoint program.
2. C
reate a new PowerPoint presentation OR open an existing PowerPoint
presentation, and within it, open the slide on which you would like to add
the video.
3. Insert the webcast DVD into the DVD drive of your computer.
4. I f a new window opens asking how you would like to view the files on the
disk, choose the option Open Folder to View Files; OR
I f a new window does not open, open the My Computer window from the
Start menu. In the My Computer window, double-click on the icon that is
shaped like a disk, which will likely be labelled D: or E:.
5.Save the video segment that you want to insert in a PowerPoint into the
same folder that contains your PowerPoint presentation.
NOTE: Video files that have been saved to your computer can be cropped
and edited into smaller segments using Movie Maker (free on PCs) or iMovie
(free on Macintosh).
6. O
pen the PowerPoint slide on which you would like to insert the video, and
click on the Insert menu in the PowerPoint menu bar.
7. F
rom the Insert menu, select Movies and Sounds, and click on the Movie
from File option.
8. A
window opens, prompting you to select the video file that you would like
to add. Find and select the video file that you saved in step 5.
9.Once you have chosen the video file you need, another window opens and
asks whether you want your movie to play either automatically when you
enter the slide, or only when it is clicked. Choose your preference.
(You will notice that the starting image of your movie is not displayed on
the slide.)
17
Printed on recycled paper
ISBN 978-1-4435-7287-3
© Queen’s Printer for Ontario, 2011